Find the System of Equations to Model the Problem

Essay

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
-In producing three types of bricks: face bricks, common bricks, and refractory bricks, a factory incurs labor,
material, and utility costs. To produce one pallet of face bricks, the labor, material, and utility costs are $50, $75,
and $35, respectively. To produce one pallet of common bricks, the labor, material, and utility costs are $50, $60,
and $30, respectively, while the corresponding costs for refractory bricks are $75, $100, and $45. In a certain
month the company has allocated $12,000 for labor costs, $14,500 for material costs and $6,000 for utility costs.
How many pallets of each type of brick should be produced in that month to exactly utilize these allocations?
Set up a system of linear equations, letting x, y, and z be the number of pallets of face, common, and refractory
bricks, respectively, that must be produced in that month.